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Master Thesis Report Literature Review Figure 2.15: Use of two control points to adjust camberline [7] curve. The thickness distribution is specified by providing a list of points for which a 2nd degree BSpline curve can be constructed. It should be pointed out that these points specifically control the thickness and not the curvature of the profile. The x values of these points represent a normalized coordinate system ranging from 0 to 1, where 0 and 1 represent the LE and TE position respectively. The y values would then represent the thickness. Optional parameters such as the number of points that control the thickness as well as a thickness factor is included in the blade modeller. The thickness factor is a parameter which scales the thickness value of all the distributed points along the camberline. The distribution of these points along the camberline can be specified by using an arctangent or simply an equispaced function. The arctangent method enables more points to be specified near the leading and trailing edge position. In addition, a stretching factor parameter is available which en- ables the user to control the actual spacing distribution of the points. Mathematically, the arctangent relation between a point distributed along the normalized axial coordinate and the ’u’ parameter is expressed as follows: u = arctan (bx) (2.44) Where ’b’ is the stretching parameter. A larger value of the stretching factor results in more points being distributed near the leading and trailing edge position. The variation of the points distributed along the ’u’ parameter with different stretching factor is illustrated in figure 2.17. Once the distri- bution of the points have been determined, the distributed points would then offset perpendicularly from the camberline with reference to the thickness value specified earlier. This process is illustrated in figure 2.18. For both the suction and pressure side curves, a B-Spline curve is used to represent the thickness distribution. The distributed points along the curve represent the thickness value used to shape the pressure and suction side curve. Therefore, by controlling the control points of the B-Spine curve, the user will be able to directly control the thickness distribution of either the suction or pressure side. Finally, the last aspect to consider is the blade profile’s leading and trailing edge shape. Within the blade modeller, the edge can be constructed by using either the radius values of the B-Spline curve (see figure 2.18) or a circular arc. The circular arc is constructed using an additional B-Spline curve based on three control points. In order to obtain the 2D blade profile, the circular arc is then connected to both the suction and pressure side curves taking G1 continuity into account. After all the 2D blade profiles have been constructed, the 3D blade can then be generated through the 17 Figure 2.16: Blade Thickness Definition [8]PDF Image | Aerodynamic Design of the NASA Rotor 67 for Non Uniform Inflow
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